Find the indicated real nth root(s) of a: n=2, a=36
Understand the Problem
The question is asking to find the real square roots (n=2) of the number 36 (a=36). This will involve determining the numbers that, when multiplied by themselves, result in 36.
Answer
The real square roots of 36 are $6$ and $-6$.
Answer for screen readers
The real square roots of 36 are $6$ and $-6$.
Steps to Solve
- Identify the nth root formula
The nth root of a number $a$ can be expressed as $a^{1/n}$. Here, we are looking for the square roots, so we have $n = 2$ and $a = 36$.
- Substitute the values into the formula
Substituting the values into the formula gives us: $$\sqrt{36} = 36^{1/2}$$
- Calculate the square root
Calculating the square root of 36 yields two results: $$\sqrt{36} = 6 \text{ and } -6$$ This is because both $6^2$ and $(-6)^2$ equal 36.
- List the real square roots
Thus, the real square roots of 36 are: $$6 \text{ and } -6$$
The real square roots of 36 are $6$ and $-6$.
More Information
The square root of a positive number will always yield two results: a positive and a negative value. The number 36 is a perfect square, making it straightforward to calculate its square roots.
Tips
- A common mistake is to only provide the positive root, forgetting that both positive and negative roots exist. Always remember that for every positive square root, there is a corresponding negative root.
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